We now explain how to prove \(\mathcal {A}(*)\lnot \rightarrow \mathcal {B}\) .
Note that if \(\mathfrak {Der} \ \mathcal {A}(\alpha ) > \mathfrak {Der} \ \mathcal {B}\)  for all \(\alpha \in I\)  then \(\mathcal {A}(*)\lnot \rightarrow \mathcal {B}\) .
One can also use the following Lemma, whose proof is the same as the proof of Lemma 1.5 from [1]}.
